Note: This worked on version 10.2.4
I received a Kindle Fire 2 today and since then I've been trying to get it rooted, now that I have I though I'd share it here for other people who might be in the same situation.
This is really just a remixing of the tool made by Bin4ry (http://forum.xda-developers.com/show....php?t=1886460) but I couldn't get the script to run on my Mac...
Step 0 - Preparing
You must enable ADB and Unknown App sources from Settings.
Settings > More > Security > Enable ADB
Settings > More > Device > Allow Installation of Applications
Step 1 is to get that tool from here. and extract it somewhere you'll remember.
Step 2 (you can skip this if you already have the android SDK platform-tools in your PATH)
If you don't have the android SDK or adb installed just add the 'stuff' folder from the tool to your path.
In terminal run
It's probably easiest if you change into the stuff folder first...
cd /Users/x/Downloads/Root_with_Restore_by_Bin4ry_v18.7z\ Folder/stuff
adb push busybox /data/local/tmp/. adb push su /data/local/tmp/. adb push Superuser.apk /data/local/tmp/. adb push ric /data/local/tmp/ric
chmod 755 /data/local/tmp/busybox exit
This requires another terminal window. Check that you can run adb from there as well (running adb should print the usage information)
In the first window run:
adb shell "while ! ln -s /data/local.prop /data/data/com.android.settings/a/file99; do :; done" > /dev/null
adb restore fakebackup.ab
You can now close the second window!
Step 5 - Cleaning Up
If it did, continue otherwise go back to step 4.
/data/local/tmp/busybox mount -o remount,rw /system /data/local/tmp/busybox mv /data/local/tmp/su /system/xbin/su /data/local/tmp/busybox mv /data/local/tmp/ric /system/bin/ric chmod 755 /system/bin/ric /data/local/tmp/busybox mv /data/local/tmp/su /system/xbin/su /data/local/tmp/busybox mv /data/local/tmp/Superuser.apk /system/app/Superuser.apk /data/local/tmp/busybox cp /data/local/tmp/busybox /system/xbin/busybox chown 0.0 /system/xbin/su && chmod 06755 /system/xbin/su chmod 655 /system/app/Superuser.apk chmod 755 /system/xbin/busybox rm /data/local.prop reboot
Update: a short guide to installing the Play store can be found here.